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Calculate the values for the 5-number summary of the skewed dataset 11, 12, 12, 13, 13, 13, 14, 14, 15, 19, 25.

The minimum value=
Quartile 1=
The median=
Quartile 3=
The maximum value=

1 answer

To calculate the 5-number summary of the dataset \(11, 12, 12, 13, 13, 13, 14, 14, 15, 19, 25\), we follow these steps:

  1. Minimum Value: This is the smallest number in the dataset.

    • Minimum = \(11\)

  2. Maximum Value: This is the largest number in the dataset.

    • Maximum = \(25\)

  3. Median: This is the middle value of the dataset. Since there are 11 values, the median is the 6th value when sorted.

    • Median = \(13\) (the 6th value)

  4. Quartile 1 (Q1): This is the median of the first half of the dataset (the first 5 values: \(11, 12, 12, 13, 13\)).

    • Q1 = Median of \(11, 12, 12, 13, 13\) which is \(12\) (the 3rd value)

  5. Quartile 3 (Q3): This is the median of the second half of the dataset (the last 5 values: \(14, 14, 15, 19, 25\)).

    • Q3 = Median of \(14, 14, 15, 19, 25\) which is \(15\) (the 3rd value)

Putting it all together, the 5-number summary is:

  • Minimum value = \(11\)
  • Quartile 1 = \(12\)
  • Median = \(13\)
  • Quartile 3 = \(15\)
  • Maximum value = \(25\)

Thus, the final results are:

  • Minimum value = 11
  • Quartile 1 = 12
  • Median = 13
  • Quartile 3 = 15
  • Maximum value = 25